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    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Formalist positions of Goodman and Quine's persuasion are refuted by reductio ad absurdum

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Under Goodman and Quine's formalism, a sentence is true or false only if a concrete proof or refutation exists
      ?

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    • 2.There exist sentences (such as the Fermat-like primality claim) that are decidable in the formal sense but for which no concrete proof or refutation exists or could be manipulated by any human
      ?

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    • 3.Under Goodman and Quine's formalism, such sentences would be neither true nor false
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Wittgenstein's rule-following considerations show that meaning requires communal practice, not abstract objects, so truth must be grounded in actual human inferential activity.
      ?

      Think about whether this reason is strong or weak

    • 2.Goodman and Quine's nominalism entails that unbounded ideal reasoners are themselves abstract posits, making 'ideal provability' an illicit platonist commitment.
      ?

      Think about whether this reason is strong or weak

    • 3.A mathematical sentence with no possible concrete proof-token has no determinate inferential role in any actual linguistic community, and therefore lacks cognitive content by verificationist standards.
      ?

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    Reason against 2 of 2
    ?
    • 1.Field's fictionalism demonstrates that classical mathematics can be conservatively dispensed with for physical applications, so preserving 'current mathematical practice' is not a decisive philosophical constraint.
      ?

      Think about whether this reason is strong or weak

    • 2.The reductio only lands if mathematical practice has normative authority over metaphysical positions, but Quine's own revisability thesis holds that no statement is immune from revision on theoretical grounds.
      ?

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    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.